Isotope shift in semiconductors with transition-metal impurities: Experiment and theory applied toZnO:Cu

Abstract

Isotope shifts for various lines associated with excitations of transition-metal impurities in semiconductors are considered. Special attention is paid to $\mathrm{Z}\mathrm{n}\mathrm{O}:\mathrm{C}\mathrm{u},$ for which experimental results are presented. Isotope shifts are measured for the so-called photoluminescence $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ zero-phonon lines associated with excitations of bound excitons, and of the zero-phonon line associated with the intracenter ${\mathrm{Cu}}^{2+}{(}^{2}{T}_{2}{\ensuremath{-}}^{2}E)$ transition. These shifts appear to be negative and nearly equal. A theoretical model explaining these results is proposed, which incorporates the mode softening mechanism and the covalent swelling of the impurity $d$ electron wave functions. It is shown that, contrary to transitions in simple neutral impurities, this mechanism works both for the excited and ground states of all processes in transition-metal impurities considered here. Using reasonable values of the parameters of the system, we are able to explain both the sign and value of the isotope shifts.